proteus 1.9.0
C/C++/Fortran libraries
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tresca.h
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1
2inline void tresca(const double& phi, const double& psi, const double& c, const double* stress, //inputs
3 double& f, double* df, double& g, double* r, double* dr) //outputs
4{
5 const int nSymTen=6,sXX=0,sYY=1,sZZ=2,sYZ=3,sZY=3,sXZ=4,sZX=4,sXY=5,sYX=5;
6 const int SKEY=0,TARGKEY=1,J3KEY=2;
7 double s,ds[nSymTen],
8 targ,dtarg[nSymTen],ddtarg[nSymTen*nSymTen],
9 J3,dJ3[nSymTen],ddJ3[nSymTen*nSymTen],
10 df_dtmp[3],
11 dg_dtmp[3],ddg_dtmp[3*3],theta;
12 const double& stress_xx(stress[sXX]),
13 stress_yy(stress[sYY]),
14 stress_zz(stress[sZZ]),
15 stress_yz(stress[sYZ]),
16 stress_zx(stress[sZX]),
17 stress_xy(stress[sXY]);
18
19 s = sqrt(3)*(stress_xx + stress_yy + stress_zz)/3;
20
21 ds[sXX] = sqrt(3)/3;
22
23 ds[sYY] = sqrt(3)/3;
24
25 ds[sZZ] = sqrt(3)/3;
26
27 ds[sYZ] = 0;
28
29 ds[sZX] = 0;
30
31 ds[sXY] = 0;
32
33 targ = 1.0e-8 + pow(stress_xx - stress_yy, 2) + pow(stress_yy - stress_zz, 2) + pow(stress_zz - stress_xx, 2) + 6*pow(stress_xy, 2) + 6*pow(stress_yz, 2) + 6*pow(stress_zx, 2);
34
35 dtarg[sXX] = -2*stress_yy - 2*stress_zz + 4*stress_xx;
36
37 dtarg[sYY] = -2*stress_xx - 2*stress_zz + 4*stress_yy;
38
39 dtarg[sZZ] = -2*stress_xx - 2*stress_yy + 4*stress_zz;
40
41 dtarg[sYZ] = 12*stress_yz;
42
43 dtarg[sZX] = 12*stress_zx;
44
45 dtarg[sXY] = 12*stress_xy;
46
47 ddtarg[sXX+ nSymTen*sXX] = 4;
48
49 ddtarg[sXX+ nSymTen*sYY] = -2;
50
51 ddtarg[sXX+ nSymTen*sZZ] = -2;
52
53 ddtarg[sXX+ nSymTen*sYZ] = 0;
54
55 ddtarg[sXX+ nSymTen*sZX] = 0;
56
57 ddtarg[sXX+ nSymTen*sXY] = 0;
58
59 ddtarg[sYY+ nSymTen*sXX] = -2;
60
61 ddtarg[sYY+ nSymTen*sYY] = 4;
62
63 ddtarg[sYY+ nSymTen*sZZ] = -2;
64
65 ddtarg[sYY+ nSymTen*sYZ] = 0;
66
67 ddtarg[sYY+ nSymTen*sZX] = 0;
68
69 ddtarg[sYY+ nSymTen*sXY] = 0;
70
71 ddtarg[sZZ+ nSymTen*sXX] = -2;
72
73 ddtarg[sZZ+ nSymTen*sYY] = -2;
74
75 ddtarg[sZZ+ nSymTen*sZZ] = 4;
76
77 ddtarg[sZZ+ nSymTen*sYZ] = 0;
78
79 ddtarg[sZZ+ nSymTen*sZX] = 0;
80
81 ddtarg[sZZ+ nSymTen*sXY] = 0;
82
83 ddtarg[sYZ+ nSymTen*sXX] = 0;
84
85 ddtarg[sYZ+ nSymTen*sYY] = 0;
86
87 ddtarg[sYZ+ nSymTen*sZZ] = 0;
88
89 ddtarg[sYZ+ nSymTen*sYZ] = 12;
90
91 ddtarg[sYZ+ nSymTen*sZX] = 0;
92
93 ddtarg[sYZ+ nSymTen*sXY] = 0;
94
95 ddtarg[sZX+ nSymTen*sXX] = 0;
96
97 ddtarg[sZX+ nSymTen*sYY] = 0;
98
99 ddtarg[sZX+ nSymTen*sZZ] = 0;
100
101 ddtarg[sZX+ nSymTen*sYZ] = 0;
102
103 ddtarg[sZX+ nSymTen*sZX] = 12;
104
105 ddtarg[sZX+ nSymTen*sXY] = 0;
106
107 ddtarg[sXY+ nSymTen*sXX] = 0;
108
109 ddtarg[sXY+ nSymTen*sYY] = 0;
110
111 ddtarg[sXY+ nSymTen*sZZ] = 0;
112
113 ddtarg[sXY+ nSymTen*sYZ] = 0;
114
115 ddtarg[sXY+ nSymTen*sZX] = 0;
116
117 ddtarg[sXY+ nSymTen*sXY] = 12;
118
119 J3 = -pow(stress_xy, 2)*(-stress_xx/3 - stress_yy/3 + 2*stress_zz/3) - pow(stress_yz, 2)*(-stress_yy/3 - stress_zz/3 + 2*stress_xx/3) - pow(stress_zx, 2)*(-stress_xx/3 - stress_zz/3 + 2*stress_yy/3) + (-stress_xx/3 - stress_zz/3 + 2*stress_yy/3)*(-stress_yy/3 - stress_zz/3 + 2*stress_xx/3)*(-stress_xx/3 - stress_yy/3 + 2*stress_zz/3) + 2*stress_xy*stress_yz*stress_zx;
120
121 dJ3[sXX] = -(-stress_xx/3 - stress_zz/3 + 2*stress_yy/3)*(-stress_yy/3 - stress_zz/3 + 2*stress_xx/3)/3 - (-stress_yy/3 - stress_zz/3 + 2*stress_xx/3)*(-stress_xx/3 - stress_yy/3 + 2*stress_zz/3)/3 + 2*(-stress_xx/3 - stress_zz/3 + 2*stress_yy/3)*(-stress_xx/3 - stress_yy/3 + 2*stress_zz/3)/3 - 2*pow(stress_yz, 2)/3 + pow(stress_xy, 2)/3 + pow(stress_zx, 2)/3;
122
123 dJ3[sYY] = -(-stress_xx/3 - stress_zz/3 + 2*stress_yy/3)*(-stress_yy/3 - stress_zz/3 + 2*stress_xx/3)/3 - (-stress_xx/3 - stress_zz/3 + 2*stress_yy/3)*(-stress_xx/3 - stress_yy/3 + 2*stress_zz/3)/3 + 2*(-stress_yy/3 - stress_zz/3 + 2*stress_xx/3)*(-stress_xx/3 - stress_yy/3 + 2*stress_zz/3)/3 - 2*pow(stress_zx, 2)/3 + pow(stress_xy, 2)/3 + pow(stress_yz, 2)/3;
124
125 dJ3[sZZ] = -(-stress_xx/3 - stress_zz/3 + 2*stress_yy/3)*(-stress_xx/3 - stress_yy/3 + 2*stress_zz/3)/3 - (-stress_yy/3 - stress_zz/3 + 2*stress_xx/3)*(-stress_xx/3 - stress_yy/3 + 2*stress_zz/3)/3 + 2*(-stress_xx/3 - stress_zz/3 + 2*stress_yy/3)*(-stress_yy/3 - stress_zz/3 + 2*stress_xx/3)/3 - 2*pow(stress_xy, 2)/3 + pow(stress_yz, 2)/3 + pow(stress_zx, 2)/3;
126
127 dJ3[sYZ] = -2*stress_yz*(-stress_yy/3 - stress_zz/3 + 2*stress_xx/3) + 2*stress_xy*stress_zx;
128
129 dJ3[sZX] = -2*stress_zx*(-stress_xx/3 - stress_zz/3 + 2*stress_yy/3) + 2*stress_xy*stress_yz;
130
131 dJ3[sXY] = -2*stress_xy*(-stress_xx/3 - stress_yy/3 + 2*stress_zz/3) + 2*stress_yz*stress_zx;
132
133 ddJ3[sXX+ nSymTen*sXX] = -2*stress_yy/9 - 2*stress_zz/9 + 4*stress_xx/9;
134
135 ddJ3[sXX+ nSymTen*sYY] = -2*stress_xx/9 - 2*stress_yy/9 + 4*stress_zz/9;
136
137 ddJ3[sXX+ nSymTen*sZZ] = -2*stress_xx/9 - 2*stress_zz/9 + 4*stress_yy/9;
138
139 ddJ3[sXX+ nSymTen*sYZ] = -4*stress_yz/3;
140
141 ddJ3[sXX+ nSymTen*sZX] = 2*stress_zx/3;
142
143 ddJ3[sXX+ nSymTen*sXY] = 2*stress_xy/3;
144
145 ddJ3[sYY+ nSymTen*sXX] = -2*stress_xx/9 - 2*stress_yy/9 + 4*stress_zz/9;
146
147 ddJ3[sYY+ nSymTen*sYY] = -2*stress_xx/9 - 2*stress_zz/9 + 4*stress_yy/9;
148
149 ddJ3[sYY+ nSymTen*sZZ] = -2*stress_yy/9 - 2*stress_zz/9 + 4*stress_xx/9;
150
151 ddJ3[sYY+ nSymTen*sYZ] = 2*stress_yz/3;
152
153 ddJ3[sYY+ nSymTen*sZX] = -4*stress_zx/3;
154
155 ddJ3[sYY+ nSymTen*sXY] = 2*stress_xy/3;
156
157 ddJ3[sZZ+ nSymTen*sXX] = -2*stress_xx/9 - 2*stress_zz/9 + 4*stress_yy/9;
158
159 ddJ3[sZZ+ nSymTen*sYY] = -2*stress_yy/9 - 2*stress_zz/9 + 4*stress_xx/9;
160
161 ddJ3[sZZ+ nSymTen*sZZ] = -2*stress_xx/9 - 2*stress_yy/9 + 4*stress_zz/9;
162
163 ddJ3[sZZ+ nSymTen*sYZ] = 2*stress_yz/3;
164
165 ddJ3[sZZ+ nSymTen*sZX] = 2*stress_zx/3;
166
167 ddJ3[sZZ+ nSymTen*sXY] = -4*stress_xy/3;
168
169 ddJ3[sYZ+ nSymTen*sXX] = -4*stress_yz/3;
170
171 ddJ3[sYZ+ nSymTen*sYY] = 2*stress_yz/3;
172
173 ddJ3[sYZ+ nSymTen*sZZ] = 2*stress_yz/3;
174
175 ddJ3[sYZ+ nSymTen*sYZ] = -4*stress_xx/3 + 2*stress_yy/3 + 2*stress_zz/3;
176
177 ddJ3[sYZ+ nSymTen*sZX] = 2*stress_xy;
178
179 ddJ3[sYZ+ nSymTen*sXY] = 2*stress_zx;
180
181 ddJ3[sZX+ nSymTen*sXX] = 2*stress_zx/3;
182
183 ddJ3[sZX+ nSymTen*sYY] = -4*stress_zx/3;
184
185 ddJ3[sZX+ nSymTen*sZZ] = 2*stress_zx/3;
186
187 ddJ3[sZX+ nSymTen*sYZ] = 2*stress_xy;
188
189 ddJ3[sZX+ nSymTen*sZX] = -4*stress_yy/3 + 2*stress_xx/3 + 2*stress_zz/3;
190
191 ddJ3[sZX+ nSymTen*sXY] = 2*stress_yz;
192
193 ddJ3[sXY+ nSymTen*sXX] = 2*stress_xy/3;
194
195 ddJ3[sXY+ nSymTen*sYY] = 2*stress_xy/3;
196
197 ddJ3[sXY+ nSymTen*sZZ] = -4*stress_xy/3;
198
199 ddJ3[sXY+ nSymTen*sYZ] = 2*stress_zx;
200
201 ddJ3[sXY+ nSymTen*sZX] = 2*stress_yz;
202
203 ddJ3[sXY+ nSymTen*sXY] = -4*stress_zz/3 + 2*stress_xx/3 + 2*stress_yy/3;
204
205 theta = -asin(27*J3*sqrt(2)/pow(targ, 3.0/2.0))/3;
206
207 f = -c + sqrt(6)*sqrt(targ)*cos(asin(27*J3*sqrt(2)/pow(targ, 3.0/2.0))/3)/6;
208
209 df_dtmp[SKEY] = 0;
210
211 df_dtmp[TARGKEY] = sqrt(6)*cos(asin(27*J3*sqrt(2)/pow(targ, 3.0/2.0))/3)/(12*sqrt(targ)) + 9*J3*sqrt(3)*sin(asin(27*J3*sqrt(2)/pow(targ, 3.0/2.0))/3)/(2*pow(targ, 2)*sqrt(1 - 1458*pow(J3, 2)/pow(targ, 3)));
212
213 df_dtmp[J3KEY] = -3*sqrt(3)*sin(asin(27*J3*sqrt(2)/pow(targ, 3.0/2.0))/3)/(targ*sqrt(1 - 1458*pow(J3, 2)/pow(targ, 3)));
214
215 df[sXX] = df_dtmp[SKEY]*ds[sXX] + df_dtmp[TARGKEY]*dtarg[sXX] + df_dtmp[J3KEY]*dJ3[sXX];
216
217 df[sYY] = df_dtmp[SKEY]*ds[sYY] + df_dtmp[TARGKEY]*dtarg[sYY] + df_dtmp[J3KEY]*dJ3[sYY];
218
219 df[sZZ] = df_dtmp[SKEY]*ds[sZZ] + df_dtmp[TARGKEY]*dtarg[sZZ] + df_dtmp[J3KEY]*dJ3[sZZ];
220
221 df[sYZ] = df_dtmp[SKEY]*ds[sYZ] + df_dtmp[TARGKEY]*dtarg[sYZ] + df_dtmp[J3KEY]*dJ3[sYZ];
222
223 df[sZX] = df_dtmp[SKEY]*ds[sZX] + df_dtmp[TARGKEY]*dtarg[sZX] + df_dtmp[J3KEY]*dJ3[sZX];
224
225 df[sXY] = df_dtmp[SKEY]*ds[sXY] + df_dtmp[TARGKEY]*dtarg[sXY] + df_dtmp[J3KEY]*dJ3[sXY];
226
227 g = -c + sqrt(6)*sqrt(targ)*cos(asin(27*J3*sqrt(2)/pow(targ, 3.0/2.0))/3)/6;
228
229 dg_dtmp[SKEY] = 0;
230
231 dg_dtmp[TARGKEY] = sqrt(6)*cos(asin(27*J3*sqrt(2)/pow(targ, 3.0/2.0))/3)/(12*sqrt(targ)) + 9*J3*sqrt(3)*sin(asin(27*J3*sqrt(2)/pow(targ, 3.0/2.0))/3)/(2*pow(targ, 2)*sqrt(1 - 1458*pow(J3, 2)/pow(targ, 3)));
232
233 dg_dtmp[J3KEY] = -3*sqrt(3)*sin(asin(27*J3*sqrt(2)/pow(targ, 3.0/2.0))/3)/(targ*sqrt(1 - 1458*pow(J3, 2)/pow(targ, 3)));
234
235 r[sXX] = dg_dtmp[SKEY]*ds[sXX] + dg_dtmp[TARGKEY]*dtarg[sXX] + dg_dtmp[J3KEY]*dJ3[sXX];
236
237 r[sYY] = dg_dtmp[SKEY]*ds[sYY] + dg_dtmp[TARGKEY]*dtarg[sYY] + dg_dtmp[J3KEY]*dJ3[sYY];
238
239 r[sZZ] = dg_dtmp[SKEY]*ds[sZZ] + dg_dtmp[TARGKEY]*dtarg[sZZ] + dg_dtmp[J3KEY]*dJ3[sZZ];
240
241 r[sYZ] = dg_dtmp[SKEY]*ds[sYZ] + dg_dtmp[TARGKEY]*dtarg[sYZ] + dg_dtmp[J3KEY]*dJ3[sYZ];
242
243 r[sZX] = dg_dtmp[SKEY]*ds[sZX] + dg_dtmp[TARGKEY]*dtarg[sZX] + dg_dtmp[J3KEY]*dJ3[sZX];
244
245 r[sXY] = dg_dtmp[SKEY]*ds[sXY] + dg_dtmp[TARGKEY]*dtarg[sXY] + dg_dtmp[J3KEY]*dJ3[sXY];
246
247 ddg_dtmp[SKEY+3*SKEY] = 0;
248
249 ddg_dtmp[SKEY+3*TARGKEY] = 0;
250
251 ddg_dtmp[SKEY+3*J3KEY] = 0;
252
253 ddg_dtmp[TARGKEY+3*SKEY] = 0;
254
255 ddg_dtmp[TARGKEY+3*TARGKEY] = -sqrt(6)*cos(asin(27*J3*sqrt(2)/pow(targ, 3.0/2.0))/3)/(24*pow(targ, 3.0/2.0)) - 19683*sqrt(3)*pow(J3, 3)*sin(asin(27*J3*sqrt(2)/pow(targ, 3.0/2.0))/3)/(2*pow(targ, 6)*pow(1 - 1458*pow(J3, 2)/pow(targ, 3), 3.0/2.0)) - 243*sqrt(6)*pow(J3, 2)*cos(asin(27*J3*sqrt(2)/pow(targ, 3.0/2.0))/3)/(4*pow(targ, 9.0/2.0)*(1 - 1458*pow(J3, 2)/pow(targ, 3))) - 27*J3*sqrt(3)*sin(asin(27*J3*sqrt(2)/pow(targ, 3.0/2.0))/3)/(4*pow(targ, 3)*sqrt(1 - 1458*pow(J3, 2)/pow(targ, 3)));
256
257 ddg_dtmp[TARGKEY+3*J3KEY] = 3*sqrt(3)*sin(asin(27*J3*sqrt(2)/pow(targ, 3.0/2.0))/3)/(pow(targ, 2)*sqrt(1 - 1458*pow(J3, 2)/pow(targ, 3))) + 6561*sqrt(3)*pow(J3, 2)*sin(asin(27*J3*sqrt(2)/pow(targ, 3.0/2.0))/3)/(pow(targ, 5)*pow(1 - 1458*pow(J3, 2)/pow(targ, 3), 3.0/2.0)) + 81*J3*sqrt(6)*cos(asin(27*J3*sqrt(2)/pow(targ, 3.0/2.0))/3)/(2*pow(targ, 7.0/2.0)*(1 - 1458*pow(J3, 2)/pow(targ, 3)));
258
259 ddg_dtmp[J3KEY+3*SKEY] = 0;
260
261 ddg_dtmp[J3KEY+3*TARGKEY] = 3*sqrt(3)*sin(asin(27*J3*sqrt(2)/pow(targ, 3.0/2.0))/3)/(pow(targ, 2)*sqrt(1 - 1458*pow(J3, 2)/pow(targ, 3))) + 6561*sqrt(3)*pow(J3, 2)*sin(asin(27*J3*sqrt(2)/pow(targ, 3.0/2.0))/3)/(pow(targ, 5)*pow(1 - 1458*pow(J3, 2)/pow(targ, 3), 3.0/2.0)) + 81*J3*sqrt(6)*cos(asin(27*J3*sqrt(2)/pow(targ, 3.0/2.0))/3)/(2*pow(targ, 7.0/2.0)*(1 - 1458*pow(J3, 2)/pow(targ, 3)));
262
263 ddg_dtmp[J3KEY+3*J3KEY] = -27*sqrt(6)*cos(asin(27*J3*sqrt(2)/pow(targ, 3.0/2.0))/3)/(pow(targ, 5.0/2.0)*(1 - 1458*pow(J3, 2)/pow(targ, 3))) - 4374*J3*sqrt(3)*sin(asin(27*J3*sqrt(2)/pow(targ, 3.0/2.0))/3)/(pow(targ, 4)*pow(1 - 1458*pow(J3, 2)/pow(targ, 3), 3.0/2.0));
264
265 dr[sXX+ nSymTen*sXX] = dg_dtmp[TARGKEY]*ddtarg[sXX+nSymTen*sXX] + dg_dtmp[J3KEY]*ddJ3[sXX+nSymTen*sXX]\
266 + ddg_dtmp[SKEY + 3*SKEY]*ds[sXX]*ds[sXX] + ddg_dtmp[SKEY + 3*TARGKEY]*dtarg[sXX]*ds[sXX] + ddg_dtmp[SKEY + 3*J3KEY]*dJ3[sXX]*ds[sXX]\
267 + ddg_dtmp[TARGKEY + 3*SKEY]*ds[sXX]*dtarg[sXX] + ddg_dtmp[TARGKEY + 3*TARGKEY]*dtarg[sXX]*dtarg[sXX] + ddg_dtmp[TARGKEY + 3*J3KEY]*dJ3[sXX]*dtarg[sXX]\
268 + ddg_dtmp[J3KEY + 3*SKEY]*ds[sXX]*dJ3[sXX] + ddg_dtmp[J3KEY + 3*TARGKEY]*dtarg[sXX]*dJ3[sXX] + ddg_dtmp[J3KEY + 3*J3KEY]*dJ3[sXX]*dJ3[sXX];
269
270 dr[sXX+ nSymTen*sYY] = dg_dtmp[TARGKEY]*ddtarg[sXX+nSymTen*sYY] + dg_dtmp[J3KEY]*ddJ3[sXX+nSymTen*sYY]\
271 + ddg_dtmp[SKEY + 3*SKEY]*ds[sYY]*ds[sXX] + ddg_dtmp[SKEY + 3*TARGKEY]*dtarg[sYY]*ds[sXX] + ddg_dtmp[SKEY + 3*J3KEY]*dJ3[sYY]*ds[sXX]\
272 + ddg_dtmp[TARGKEY + 3*SKEY]*ds[sYY]*dtarg[sXX] + ddg_dtmp[TARGKEY + 3*TARGKEY]*dtarg[sYY]*dtarg[sXX] + ddg_dtmp[TARGKEY + 3*J3KEY]*dJ3[sYY]*dtarg[sXX]\
273 + ddg_dtmp[J3KEY + 3*SKEY]*ds[sYY]*dJ3[sXX] + ddg_dtmp[J3KEY + 3*TARGKEY]*dtarg[sYY]*dJ3[sXX] + ddg_dtmp[J3KEY + 3*J3KEY]*dJ3[sYY]*dJ3[sXX];
274
275 dr[sXX+ nSymTen*sZZ] = dg_dtmp[TARGKEY]*ddtarg[sXX+nSymTen*sZZ] + dg_dtmp[J3KEY]*ddJ3[sXX+nSymTen*sZZ]\
276 + ddg_dtmp[SKEY + 3*SKEY]*ds[sZZ]*ds[sXX] + ddg_dtmp[SKEY + 3*TARGKEY]*dtarg[sZZ]*ds[sXX] + ddg_dtmp[SKEY + 3*J3KEY]*dJ3[sZZ]*ds[sXX]\
277 + ddg_dtmp[TARGKEY + 3*SKEY]*ds[sZZ]*dtarg[sXX] + ddg_dtmp[TARGKEY + 3*TARGKEY]*dtarg[sZZ]*dtarg[sXX] + ddg_dtmp[TARGKEY + 3*J3KEY]*dJ3[sZZ]*dtarg[sXX]\
278 + ddg_dtmp[J3KEY + 3*SKEY]*ds[sZZ]*dJ3[sXX] + ddg_dtmp[J3KEY + 3*TARGKEY]*dtarg[sZZ]*dJ3[sXX] + ddg_dtmp[J3KEY + 3*J3KEY]*dJ3[sZZ]*dJ3[sXX];
279
280 dr[sXX+ nSymTen*sYZ] = dg_dtmp[TARGKEY]*ddtarg[sXX+nSymTen*sYZ] + dg_dtmp[J3KEY]*ddJ3[sXX+nSymTen*sYZ]\
281 + ddg_dtmp[SKEY + 3*SKEY]*ds[sYZ]*ds[sXX] + ddg_dtmp[SKEY + 3*TARGKEY]*dtarg[sYZ]*ds[sXX] + ddg_dtmp[SKEY + 3*J3KEY]*dJ3[sYZ]*ds[sXX]\
282 + ddg_dtmp[TARGKEY + 3*SKEY]*ds[sYZ]*dtarg[sXX] + ddg_dtmp[TARGKEY + 3*TARGKEY]*dtarg[sYZ]*dtarg[sXX] + ddg_dtmp[TARGKEY + 3*J3KEY]*dJ3[sYZ]*dtarg[sXX]\
283 + ddg_dtmp[J3KEY + 3*SKEY]*ds[sYZ]*dJ3[sXX] + ddg_dtmp[J3KEY + 3*TARGKEY]*dtarg[sYZ]*dJ3[sXX] + ddg_dtmp[J3KEY + 3*J3KEY]*dJ3[sYZ]*dJ3[sXX];
284
285 dr[sXX+ nSymTen*sZX] = dg_dtmp[TARGKEY]*ddtarg[sXX+nSymTen*sZX] + dg_dtmp[J3KEY]*ddJ3[sXX+nSymTen*sZX]\
286 + ddg_dtmp[SKEY + 3*SKEY]*ds[sZX]*ds[sXX] + ddg_dtmp[SKEY + 3*TARGKEY]*dtarg[sZX]*ds[sXX] + ddg_dtmp[SKEY + 3*J3KEY]*dJ3[sZX]*ds[sXX]\
287 + ddg_dtmp[TARGKEY + 3*SKEY]*ds[sZX]*dtarg[sXX] + ddg_dtmp[TARGKEY + 3*TARGKEY]*dtarg[sZX]*dtarg[sXX] + ddg_dtmp[TARGKEY + 3*J3KEY]*dJ3[sZX]*dtarg[sXX]\
288 + ddg_dtmp[J3KEY + 3*SKEY]*ds[sZX]*dJ3[sXX] + ddg_dtmp[J3KEY + 3*TARGKEY]*dtarg[sZX]*dJ3[sXX] + ddg_dtmp[J3KEY + 3*J3KEY]*dJ3[sZX]*dJ3[sXX];
289
290 dr[sXX+ nSymTen*sXY] = dg_dtmp[TARGKEY]*ddtarg[sXX+nSymTen*sXY] + dg_dtmp[J3KEY]*ddJ3[sXX+nSymTen*sXY]\
291 + ddg_dtmp[SKEY + 3*SKEY]*ds[sXY]*ds[sXX] + ddg_dtmp[SKEY + 3*TARGKEY]*dtarg[sXY]*ds[sXX] + ddg_dtmp[SKEY + 3*J3KEY]*dJ3[sXY]*ds[sXX]\
292 + ddg_dtmp[TARGKEY + 3*SKEY]*ds[sXY]*dtarg[sXX] + ddg_dtmp[TARGKEY + 3*TARGKEY]*dtarg[sXY]*dtarg[sXX] + ddg_dtmp[TARGKEY + 3*J3KEY]*dJ3[sXY]*dtarg[sXX]\
293 + ddg_dtmp[J3KEY + 3*SKEY]*ds[sXY]*dJ3[sXX] + ddg_dtmp[J3KEY + 3*TARGKEY]*dtarg[sXY]*dJ3[sXX] + ddg_dtmp[J3KEY + 3*J3KEY]*dJ3[sXY]*dJ3[sXX];
294
295 dr[sYY+ nSymTen*sXX] = dg_dtmp[TARGKEY]*ddtarg[sYY+nSymTen*sXX] + dg_dtmp[J3KEY]*ddJ3[sYY+nSymTen*sXX]\
296 + ddg_dtmp[SKEY + 3*SKEY]*ds[sXX]*ds[sYY] + ddg_dtmp[SKEY + 3*TARGKEY]*dtarg[sXX]*ds[sYY] + ddg_dtmp[SKEY + 3*J3KEY]*dJ3[sXX]*ds[sYY]\
297 + ddg_dtmp[TARGKEY + 3*SKEY]*ds[sXX]*dtarg[sYY] + ddg_dtmp[TARGKEY + 3*TARGKEY]*dtarg[sXX]*dtarg[sYY] + ddg_dtmp[TARGKEY + 3*J3KEY]*dJ3[sXX]*dtarg[sYY]\
298 + ddg_dtmp[J3KEY + 3*SKEY]*ds[sXX]*dJ3[sYY] + ddg_dtmp[J3KEY + 3*TARGKEY]*dtarg[sXX]*dJ3[sYY] + ddg_dtmp[J3KEY + 3*J3KEY]*dJ3[sXX]*dJ3[sYY];
299
300 dr[sYY+ nSymTen*sYY] = dg_dtmp[TARGKEY]*ddtarg[sYY+nSymTen*sYY] + dg_dtmp[J3KEY]*ddJ3[sYY+nSymTen*sYY]\
301 + ddg_dtmp[SKEY + 3*SKEY]*ds[sYY]*ds[sYY] + ddg_dtmp[SKEY + 3*TARGKEY]*dtarg[sYY]*ds[sYY] + ddg_dtmp[SKEY + 3*J3KEY]*dJ3[sYY]*ds[sYY]\
302 + ddg_dtmp[TARGKEY + 3*SKEY]*ds[sYY]*dtarg[sYY] + ddg_dtmp[TARGKEY + 3*TARGKEY]*dtarg[sYY]*dtarg[sYY] + ddg_dtmp[TARGKEY + 3*J3KEY]*dJ3[sYY]*dtarg[sYY]\
303 + ddg_dtmp[J3KEY + 3*SKEY]*ds[sYY]*dJ3[sYY] + ddg_dtmp[J3KEY + 3*TARGKEY]*dtarg[sYY]*dJ3[sYY] + ddg_dtmp[J3KEY + 3*J3KEY]*dJ3[sYY]*dJ3[sYY];
304
305 dr[sYY+ nSymTen*sZZ] = dg_dtmp[TARGKEY]*ddtarg[sYY+nSymTen*sZZ] + dg_dtmp[J3KEY]*ddJ3[sYY+nSymTen*sZZ]\
306 + ddg_dtmp[SKEY + 3*SKEY]*ds[sZZ]*ds[sYY] + ddg_dtmp[SKEY + 3*TARGKEY]*dtarg[sZZ]*ds[sYY] + ddg_dtmp[SKEY + 3*J3KEY]*dJ3[sZZ]*ds[sYY]\
307 + ddg_dtmp[TARGKEY + 3*SKEY]*ds[sZZ]*dtarg[sYY] + ddg_dtmp[TARGKEY + 3*TARGKEY]*dtarg[sZZ]*dtarg[sYY] + ddg_dtmp[TARGKEY + 3*J3KEY]*dJ3[sZZ]*dtarg[sYY]\
308 + ddg_dtmp[J3KEY + 3*SKEY]*ds[sZZ]*dJ3[sYY] + ddg_dtmp[J3KEY + 3*TARGKEY]*dtarg[sZZ]*dJ3[sYY] + ddg_dtmp[J3KEY + 3*J3KEY]*dJ3[sZZ]*dJ3[sYY];
309
310 dr[sYY+ nSymTen*sYZ] = dg_dtmp[TARGKEY]*ddtarg[sYY+nSymTen*sYZ] + dg_dtmp[J3KEY]*ddJ3[sYY+nSymTen*sYZ]\
311 + ddg_dtmp[SKEY + 3*SKEY]*ds[sYZ]*ds[sYY] + ddg_dtmp[SKEY + 3*TARGKEY]*dtarg[sYZ]*ds[sYY] + ddg_dtmp[SKEY + 3*J3KEY]*dJ3[sYZ]*ds[sYY]\
312 + ddg_dtmp[TARGKEY + 3*SKEY]*ds[sYZ]*dtarg[sYY] + ddg_dtmp[TARGKEY + 3*TARGKEY]*dtarg[sYZ]*dtarg[sYY] + ddg_dtmp[TARGKEY + 3*J3KEY]*dJ3[sYZ]*dtarg[sYY]\
313 + ddg_dtmp[J3KEY + 3*SKEY]*ds[sYZ]*dJ3[sYY] + ddg_dtmp[J3KEY + 3*TARGKEY]*dtarg[sYZ]*dJ3[sYY] + ddg_dtmp[J3KEY + 3*J3KEY]*dJ3[sYZ]*dJ3[sYY];
314
315 dr[sYY+ nSymTen*sZX] = dg_dtmp[TARGKEY]*ddtarg[sYY+nSymTen*sZX] + dg_dtmp[J3KEY]*ddJ3[sYY+nSymTen*sZX]\
316 + ddg_dtmp[SKEY + 3*SKEY]*ds[sZX]*ds[sYY] + ddg_dtmp[SKEY + 3*TARGKEY]*dtarg[sZX]*ds[sYY] + ddg_dtmp[SKEY + 3*J3KEY]*dJ3[sZX]*ds[sYY]\
317 + ddg_dtmp[TARGKEY + 3*SKEY]*ds[sZX]*dtarg[sYY] + ddg_dtmp[TARGKEY + 3*TARGKEY]*dtarg[sZX]*dtarg[sYY] + ddg_dtmp[TARGKEY + 3*J3KEY]*dJ3[sZX]*dtarg[sYY]\
318 + ddg_dtmp[J3KEY + 3*SKEY]*ds[sZX]*dJ3[sYY] + ddg_dtmp[J3KEY + 3*TARGKEY]*dtarg[sZX]*dJ3[sYY] + ddg_dtmp[J3KEY + 3*J3KEY]*dJ3[sZX]*dJ3[sYY];
319
320 dr[sYY+ nSymTen*sXY] = dg_dtmp[TARGKEY]*ddtarg[sYY+nSymTen*sXY] + dg_dtmp[J3KEY]*ddJ3[sYY+nSymTen*sXY]\
321 + ddg_dtmp[SKEY + 3*SKEY]*ds[sXY]*ds[sYY] + ddg_dtmp[SKEY + 3*TARGKEY]*dtarg[sXY]*ds[sYY] + ddg_dtmp[SKEY + 3*J3KEY]*dJ3[sXY]*ds[sYY]\
322 + ddg_dtmp[TARGKEY + 3*SKEY]*ds[sXY]*dtarg[sYY] + ddg_dtmp[TARGKEY + 3*TARGKEY]*dtarg[sXY]*dtarg[sYY] + ddg_dtmp[TARGKEY + 3*J3KEY]*dJ3[sXY]*dtarg[sYY]\
323 + ddg_dtmp[J3KEY + 3*SKEY]*ds[sXY]*dJ3[sYY] + ddg_dtmp[J3KEY + 3*TARGKEY]*dtarg[sXY]*dJ3[sYY] + ddg_dtmp[J3KEY + 3*J3KEY]*dJ3[sXY]*dJ3[sYY];
324
325 dr[sZZ+ nSymTen*sXX] = dg_dtmp[TARGKEY]*ddtarg[sZZ+nSymTen*sXX] + dg_dtmp[J3KEY]*ddJ3[sZZ+nSymTen*sXX]\
326 + ddg_dtmp[SKEY + 3*SKEY]*ds[sXX]*ds[sZZ] + ddg_dtmp[SKEY + 3*TARGKEY]*dtarg[sXX]*ds[sZZ] + ddg_dtmp[SKEY + 3*J3KEY]*dJ3[sXX]*ds[sZZ]\
327 + ddg_dtmp[TARGKEY + 3*SKEY]*ds[sXX]*dtarg[sZZ] + ddg_dtmp[TARGKEY + 3*TARGKEY]*dtarg[sXX]*dtarg[sZZ] + ddg_dtmp[TARGKEY + 3*J3KEY]*dJ3[sXX]*dtarg[sZZ]\
328 + ddg_dtmp[J3KEY + 3*SKEY]*ds[sXX]*dJ3[sZZ] + ddg_dtmp[J3KEY + 3*TARGKEY]*dtarg[sXX]*dJ3[sZZ] + ddg_dtmp[J3KEY + 3*J3KEY]*dJ3[sXX]*dJ3[sZZ];
329
330 dr[sZZ+ nSymTen*sYY] = dg_dtmp[TARGKEY]*ddtarg[sZZ+nSymTen*sYY] + dg_dtmp[J3KEY]*ddJ3[sZZ+nSymTen*sYY]\
331 + ddg_dtmp[SKEY + 3*SKEY]*ds[sYY]*ds[sZZ] + ddg_dtmp[SKEY + 3*TARGKEY]*dtarg[sYY]*ds[sZZ] + ddg_dtmp[SKEY + 3*J3KEY]*dJ3[sYY]*ds[sZZ]\
332 + ddg_dtmp[TARGKEY + 3*SKEY]*ds[sYY]*dtarg[sZZ] + ddg_dtmp[TARGKEY + 3*TARGKEY]*dtarg[sYY]*dtarg[sZZ] + ddg_dtmp[TARGKEY + 3*J3KEY]*dJ3[sYY]*dtarg[sZZ]\
333 + ddg_dtmp[J3KEY + 3*SKEY]*ds[sYY]*dJ3[sZZ] + ddg_dtmp[J3KEY + 3*TARGKEY]*dtarg[sYY]*dJ3[sZZ] + ddg_dtmp[J3KEY + 3*J3KEY]*dJ3[sYY]*dJ3[sZZ];
334
335 dr[sZZ+ nSymTen*sZZ] = dg_dtmp[TARGKEY]*ddtarg[sZZ+nSymTen*sZZ] + dg_dtmp[J3KEY]*ddJ3[sZZ+nSymTen*sZZ]\
336 + ddg_dtmp[SKEY + 3*SKEY]*ds[sZZ]*ds[sZZ] + ddg_dtmp[SKEY + 3*TARGKEY]*dtarg[sZZ]*ds[sZZ] + ddg_dtmp[SKEY + 3*J3KEY]*dJ3[sZZ]*ds[sZZ]\
337 + ddg_dtmp[TARGKEY + 3*SKEY]*ds[sZZ]*dtarg[sZZ] + ddg_dtmp[TARGKEY + 3*TARGKEY]*dtarg[sZZ]*dtarg[sZZ] + ddg_dtmp[TARGKEY + 3*J3KEY]*dJ3[sZZ]*dtarg[sZZ]\
338 + ddg_dtmp[J3KEY + 3*SKEY]*ds[sZZ]*dJ3[sZZ] + ddg_dtmp[J3KEY + 3*TARGKEY]*dtarg[sZZ]*dJ3[sZZ] + ddg_dtmp[J3KEY + 3*J3KEY]*dJ3[sZZ]*dJ3[sZZ];
339
340 dr[sZZ+ nSymTen*sYZ] = dg_dtmp[TARGKEY]*ddtarg[sZZ+nSymTen*sYZ] + dg_dtmp[J3KEY]*ddJ3[sZZ+nSymTen*sYZ]\
341 + ddg_dtmp[SKEY + 3*SKEY]*ds[sYZ]*ds[sZZ] + ddg_dtmp[SKEY + 3*TARGKEY]*dtarg[sYZ]*ds[sZZ] + ddg_dtmp[SKEY + 3*J3KEY]*dJ3[sYZ]*ds[sZZ]\
342 + ddg_dtmp[TARGKEY + 3*SKEY]*ds[sYZ]*dtarg[sZZ] + ddg_dtmp[TARGKEY + 3*TARGKEY]*dtarg[sYZ]*dtarg[sZZ] + ddg_dtmp[TARGKEY + 3*J3KEY]*dJ3[sYZ]*dtarg[sZZ]\
343 + ddg_dtmp[J3KEY + 3*SKEY]*ds[sYZ]*dJ3[sZZ] + ddg_dtmp[J3KEY + 3*TARGKEY]*dtarg[sYZ]*dJ3[sZZ] + ddg_dtmp[J3KEY + 3*J3KEY]*dJ3[sYZ]*dJ3[sZZ];
344
345 dr[sZZ+ nSymTen*sZX] = dg_dtmp[TARGKEY]*ddtarg[sZZ+nSymTen*sZX] + dg_dtmp[J3KEY]*ddJ3[sZZ+nSymTen*sZX]\
346 + ddg_dtmp[SKEY + 3*SKEY]*ds[sZX]*ds[sZZ] + ddg_dtmp[SKEY + 3*TARGKEY]*dtarg[sZX]*ds[sZZ] + ddg_dtmp[SKEY + 3*J3KEY]*dJ3[sZX]*ds[sZZ]\
347 + ddg_dtmp[TARGKEY + 3*SKEY]*ds[sZX]*dtarg[sZZ] + ddg_dtmp[TARGKEY + 3*TARGKEY]*dtarg[sZX]*dtarg[sZZ] + ddg_dtmp[TARGKEY + 3*J3KEY]*dJ3[sZX]*dtarg[sZZ]\
348 + ddg_dtmp[J3KEY + 3*SKEY]*ds[sZX]*dJ3[sZZ] + ddg_dtmp[J3KEY + 3*TARGKEY]*dtarg[sZX]*dJ3[sZZ] + ddg_dtmp[J3KEY + 3*J3KEY]*dJ3[sZX]*dJ3[sZZ];
349
350 dr[sZZ+ nSymTen*sXY] = dg_dtmp[TARGKEY]*ddtarg[sZZ+nSymTen*sXY] + dg_dtmp[J3KEY]*ddJ3[sZZ+nSymTen*sXY]\
351 + ddg_dtmp[SKEY + 3*SKEY]*ds[sXY]*ds[sZZ] + ddg_dtmp[SKEY + 3*TARGKEY]*dtarg[sXY]*ds[sZZ] + ddg_dtmp[SKEY + 3*J3KEY]*dJ3[sXY]*ds[sZZ]\
352 + ddg_dtmp[TARGKEY + 3*SKEY]*ds[sXY]*dtarg[sZZ] + ddg_dtmp[TARGKEY + 3*TARGKEY]*dtarg[sXY]*dtarg[sZZ] + ddg_dtmp[TARGKEY + 3*J3KEY]*dJ3[sXY]*dtarg[sZZ]\
353 + ddg_dtmp[J3KEY + 3*SKEY]*ds[sXY]*dJ3[sZZ] + ddg_dtmp[J3KEY + 3*TARGKEY]*dtarg[sXY]*dJ3[sZZ] + ddg_dtmp[J3KEY + 3*J3KEY]*dJ3[sXY]*dJ3[sZZ];
354
355 dr[sYZ+ nSymTen*sXX] = dg_dtmp[TARGKEY]*ddtarg[sYZ+nSymTen*sXX] + dg_dtmp[J3KEY]*ddJ3[sYZ+nSymTen*sXX]\
356 + ddg_dtmp[SKEY + 3*SKEY]*ds[sXX]*ds[sYZ] + ddg_dtmp[SKEY + 3*TARGKEY]*dtarg[sXX]*ds[sYZ] + ddg_dtmp[SKEY + 3*J3KEY]*dJ3[sXX]*ds[sYZ]\
357 + ddg_dtmp[TARGKEY + 3*SKEY]*ds[sXX]*dtarg[sYZ] + ddg_dtmp[TARGKEY + 3*TARGKEY]*dtarg[sXX]*dtarg[sYZ] + ddg_dtmp[TARGKEY + 3*J3KEY]*dJ3[sXX]*dtarg[sYZ]\
358 + ddg_dtmp[J3KEY + 3*SKEY]*ds[sXX]*dJ3[sYZ] + ddg_dtmp[J3KEY + 3*TARGKEY]*dtarg[sXX]*dJ3[sYZ] + ddg_dtmp[J3KEY + 3*J3KEY]*dJ3[sXX]*dJ3[sYZ];
359
360 dr[sYZ+ nSymTen*sYY] = dg_dtmp[TARGKEY]*ddtarg[sYZ+nSymTen*sYY] + dg_dtmp[J3KEY]*ddJ3[sYZ+nSymTen*sYY]\
361 + ddg_dtmp[SKEY + 3*SKEY]*ds[sYY]*ds[sYZ] + ddg_dtmp[SKEY + 3*TARGKEY]*dtarg[sYY]*ds[sYZ] + ddg_dtmp[SKEY + 3*J3KEY]*dJ3[sYY]*ds[sYZ]\
362 + ddg_dtmp[TARGKEY + 3*SKEY]*ds[sYY]*dtarg[sYZ] + ddg_dtmp[TARGKEY + 3*TARGKEY]*dtarg[sYY]*dtarg[sYZ] + ddg_dtmp[TARGKEY + 3*J3KEY]*dJ3[sYY]*dtarg[sYZ]\
363 + ddg_dtmp[J3KEY + 3*SKEY]*ds[sYY]*dJ3[sYZ] + ddg_dtmp[J3KEY + 3*TARGKEY]*dtarg[sYY]*dJ3[sYZ] + ddg_dtmp[J3KEY + 3*J3KEY]*dJ3[sYY]*dJ3[sYZ];
364
365 dr[sYZ+ nSymTen*sZZ] = dg_dtmp[TARGKEY]*ddtarg[sYZ+nSymTen*sZZ] + dg_dtmp[J3KEY]*ddJ3[sYZ+nSymTen*sZZ]\
366 + ddg_dtmp[SKEY + 3*SKEY]*ds[sZZ]*ds[sYZ] + ddg_dtmp[SKEY + 3*TARGKEY]*dtarg[sZZ]*ds[sYZ] + ddg_dtmp[SKEY + 3*J3KEY]*dJ3[sZZ]*ds[sYZ]\
367 + ddg_dtmp[TARGKEY + 3*SKEY]*ds[sZZ]*dtarg[sYZ] + ddg_dtmp[TARGKEY + 3*TARGKEY]*dtarg[sZZ]*dtarg[sYZ] + ddg_dtmp[TARGKEY + 3*J3KEY]*dJ3[sZZ]*dtarg[sYZ]\
368 + ddg_dtmp[J3KEY + 3*SKEY]*ds[sZZ]*dJ3[sYZ] + ddg_dtmp[J3KEY + 3*TARGKEY]*dtarg[sZZ]*dJ3[sYZ] + ddg_dtmp[J3KEY + 3*J3KEY]*dJ3[sZZ]*dJ3[sYZ];
369
370 dr[sYZ+ nSymTen*sYZ] = dg_dtmp[TARGKEY]*ddtarg[sYZ+nSymTen*sYZ] + dg_dtmp[J3KEY]*ddJ3[sYZ+nSymTen*sYZ]\
371 + ddg_dtmp[SKEY + 3*SKEY]*ds[sYZ]*ds[sYZ] + ddg_dtmp[SKEY + 3*TARGKEY]*dtarg[sYZ]*ds[sYZ] + ddg_dtmp[SKEY + 3*J3KEY]*dJ3[sYZ]*ds[sYZ]\
372 + ddg_dtmp[TARGKEY + 3*SKEY]*ds[sYZ]*dtarg[sYZ] + ddg_dtmp[TARGKEY + 3*TARGKEY]*dtarg[sYZ]*dtarg[sYZ] + ddg_dtmp[TARGKEY + 3*J3KEY]*dJ3[sYZ]*dtarg[sYZ]\
373 + ddg_dtmp[J3KEY + 3*SKEY]*ds[sYZ]*dJ3[sYZ] + ddg_dtmp[J3KEY + 3*TARGKEY]*dtarg[sYZ]*dJ3[sYZ] + ddg_dtmp[J3KEY + 3*J3KEY]*dJ3[sYZ]*dJ3[sYZ];
374
375 dr[sYZ+ nSymTen*sZX] = dg_dtmp[TARGKEY]*ddtarg[sYZ+nSymTen*sZX] + dg_dtmp[J3KEY]*ddJ3[sYZ+nSymTen*sZX]\
376 + ddg_dtmp[SKEY + 3*SKEY]*ds[sZX]*ds[sYZ] + ddg_dtmp[SKEY + 3*TARGKEY]*dtarg[sZX]*ds[sYZ] + ddg_dtmp[SKEY + 3*J3KEY]*dJ3[sZX]*ds[sYZ]\
377 + ddg_dtmp[TARGKEY + 3*SKEY]*ds[sZX]*dtarg[sYZ] + ddg_dtmp[TARGKEY + 3*TARGKEY]*dtarg[sZX]*dtarg[sYZ] + ddg_dtmp[TARGKEY + 3*J3KEY]*dJ3[sZX]*dtarg[sYZ]\
378 + ddg_dtmp[J3KEY + 3*SKEY]*ds[sZX]*dJ3[sYZ] + ddg_dtmp[J3KEY + 3*TARGKEY]*dtarg[sZX]*dJ3[sYZ] + ddg_dtmp[J3KEY + 3*J3KEY]*dJ3[sZX]*dJ3[sYZ];
379
380 dr[sYZ+ nSymTen*sXY] = dg_dtmp[TARGKEY]*ddtarg[sYZ+nSymTen*sXY] + dg_dtmp[J3KEY]*ddJ3[sYZ+nSymTen*sXY]\
381 + ddg_dtmp[SKEY + 3*SKEY]*ds[sXY]*ds[sYZ] + ddg_dtmp[SKEY + 3*TARGKEY]*dtarg[sXY]*ds[sYZ] + ddg_dtmp[SKEY + 3*J3KEY]*dJ3[sXY]*ds[sYZ]\
382 + ddg_dtmp[TARGKEY + 3*SKEY]*ds[sXY]*dtarg[sYZ] + ddg_dtmp[TARGKEY + 3*TARGKEY]*dtarg[sXY]*dtarg[sYZ] + ddg_dtmp[TARGKEY + 3*J3KEY]*dJ3[sXY]*dtarg[sYZ]\
383 + ddg_dtmp[J3KEY + 3*SKEY]*ds[sXY]*dJ3[sYZ] + ddg_dtmp[J3KEY + 3*TARGKEY]*dtarg[sXY]*dJ3[sYZ] + ddg_dtmp[J3KEY + 3*J3KEY]*dJ3[sXY]*dJ3[sYZ];
384
385 dr[sZX+ nSymTen*sXX] = dg_dtmp[TARGKEY]*ddtarg[sZX+nSymTen*sXX] + dg_dtmp[J3KEY]*ddJ3[sZX+nSymTen*sXX]\
386 + ddg_dtmp[SKEY + 3*SKEY]*ds[sXX]*ds[sZX] + ddg_dtmp[SKEY + 3*TARGKEY]*dtarg[sXX]*ds[sZX] + ddg_dtmp[SKEY + 3*J3KEY]*dJ3[sXX]*ds[sZX]\
387 + ddg_dtmp[TARGKEY + 3*SKEY]*ds[sXX]*dtarg[sZX] + ddg_dtmp[TARGKEY + 3*TARGKEY]*dtarg[sXX]*dtarg[sZX] + ddg_dtmp[TARGKEY + 3*J3KEY]*dJ3[sXX]*dtarg[sZX]\
388 + ddg_dtmp[J3KEY + 3*SKEY]*ds[sXX]*dJ3[sZX] + ddg_dtmp[J3KEY + 3*TARGKEY]*dtarg[sXX]*dJ3[sZX] + ddg_dtmp[J3KEY + 3*J3KEY]*dJ3[sXX]*dJ3[sZX];
389
390 dr[sZX+ nSymTen*sYY] = dg_dtmp[TARGKEY]*ddtarg[sZX+nSymTen*sYY] + dg_dtmp[J3KEY]*ddJ3[sZX+nSymTen*sYY]\
391 + ddg_dtmp[SKEY + 3*SKEY]*ds[sYY]*ds[sZX] + ddg_dtmp[SKEY + 3*TARGKEY]*dtarg[sYY]*ds[sZX] + ddg_dtmp[SKEY + 3*J3KEY]*dJ3[sYY]*ds[sZX]\
392 + ddg_dtmp[TARGKEY + 3*SKEY]*ds[sYY]*dtarg[sZX] + ddg_dtmp[TARGKEY + 3*TARGKEY]*dtarg[sYY]*dtarg[sZX] + ddg_dtmp[TARGKEY + 3*J3KEY]*dJ3[sYY]*dtarg[sZX]\
393 + ddg_dtmp[J3KEY + 3*SKEY]*ds[sYY]*dJ3[sZX] + ddg_dtmp[J3KEY + 3*TARGKEY]*dtarg[sYY]*dJ3[sZX] + ddg_dtmp[J3KEY + 3*J3KEY]*dJ3[sYY]*dJ3[sZX];
394
395 dr[sZX+ nSymTen*sZZ] = dg_dtmp[TARGKEY]*ddtarg[sZX+nSymTen*sZZ] + dg_dtmp[J3KEY]*ddJ3[sZX+nSymTen*sZZ]\
396 + ddg_dtmp[SKEY + 3*SKEY]*ds[sZZ]*ds[sZX] + ddg_dtmp[SKEY + 3*TARGKEY]*dtarg[sZZ]*ds[sZX] + ddg_dtmp[SKEY + 3*J3KEY]*dJ3[sZZ]*ds[sZX]\
397 + ddg_dtmp[TARGKEY + 3*SKEY]*ds[sZZ]*dtarg[sZX] + ddg_dtmp[TARGKEY + 3*TARGKEY]*dtarg[sZZ]*dtarg[sZX] + ddg_dtmp[TARGKEY + 3*J3KEY]*dJ3[sZZ]*dtarg[sZX]\
398 + ddg_dtmp[J3KEY + 3*SKEY]*ds[sZZ]*dJ3[sZX] + ddg_dtmp[J3KEY + 3*TARGKEY]*dtarg[sZZ]*dJ3[sZX] + ddg_dtmp[J3KEY + 3*J3KEY]*dJ3[sZZ]*dJ3[sZX];
399
400 dr[sZX+ nSymTen*sYZ] = dg_dtmp[TARGKEY]*ddtarg[sZX+nSymTen*sYZ] + dg_dtmp[J3KEY]*ddJ3[sZX+nSymTen*sYZ]\
401 + ddg_dtmp[SKEY + 3*SKEY]*ds[sYZ]*ds[sZX] + ddg_dtmp[SKEY + 3*TARGKEY]*dtarg[sYZ]*ds[sZX] + ddg_dtmp[SKEY + 3*J3KEY]*dJ3[sYZ]*ds[sZX]\
402 + ddg_dtmp[TARGKEY + 3*SKEY]*ds[sYZ]*dtarg[sZX] + ddg_dtmp[TARGKEY + 3*TARGKEY]*dtarg[sYZ]*dtarg[sZX] + ddg_dtmp[TARGKEY + 3*J3KEY]*dJ3[sYZ]*dtarg[sZX]\
403 + ddg_dtmp[J3KEY + 3*SKEY]*ds[sYZ]*dJ3[sZX] + ddg_dtmp[J3KEY + 3*TARGKEY]*dtarg[sYZ]*dJ3[sZX] + ddg_dtmp[J3KEY + 3*J3KEY]*dJ3[sYZ]*dJ3[sZX];
404
405 dr[sZX+ nSymTen*sZX] = dg_dtmp[TARGKEY]*ddtarg[sZX+nSymTen*sZX] + dg_dtmp[J3KEY]*ddJ3[sZX+nSymTen*sZX]\
406 + ddg_dtmp[SKEY + 3*SKEY]*ds[sZX]*ds[sZX] + ddg_dtmp[SKEY + 3*TARGKEY]*dtarg[sZX]*ds[sZX] + ddg_dtmp[SKEY + 3*J3KEY]*dJ3[sZX]*ds[sZX]\
407 + ddg_dtmp[TARGKEY + 3*SKEY]*ds[sZX]*dtarg[sZX] + ddg_dtmp[TARGKEY + 3*TARGKEY]*dtarg[sZX]*dtarg[sZX] + ddg_dtmp[TARGKEY + 3*J3KEY]*dJ3[sZX]*dtarg[sZX]\
408 + ddg_dtmp[J3KEY + 3*SKEY]*ds[sZX]*dJ3[sZX] + ddg_dtmp[J3KEY + 3*TARGKEY]*dtarg[sZX]*dJ3[sZX] + ddg_dtmp[J3KEY + 3*J3KEY]*dJ3[sZX]*dJ3[sZX];
409
410 dr[sZX+ nSymTen*sXY] = dg_dtmp[TARGKEY]*ddtarg[sZX+nSymTen*sXY] + dg_dtmp[J3KEY]*ddJ3[sZX+nSymTen*sXY]\
411 + ddg_dtmp[SKEY + 3*SKEY]*ds[sXY]*ds[sZX] + ddg_dtmp[SKEY + 3*TARGKEY]*dtarg[sXY]*ds[sZX] + ddg_dtmp[SKEY + 3*J3KEY]*dJ3[sXY]*ds[sZX]\
412 + ddg_dtmp[TARGKEY + 3*SKEY]*ds[sXY]*dtarg[sZX] + ddg_dtmp[TARGKEY + 3*TARGKEY]*dtarg[sXY]*dtarg[sZX] + ddg_dtmp[TARGKEY + 3*J3KEY]*dJ3[sXY]*dtarg[sZX]\
413 + ddg_dtmp[J3KEY + 3*SKEY]*ds[sXY]*dJ3[sZX] + ddg_dtmp[J3KEY + 3*TARGKEY]*dtarg[sXY]*dJ3[sZX] + ddg_dtmp[J3KEY + 3*J3KEY]*dJ3[sXY]*dJ3[sZX];
414
415 dr[sXY+ nSymTen*sXX] = dg_dtmp[TARGKEY]*ddtarg[sXY+nSymTen*sXX] + dg_dtmp[J3KEY]*ddJ3[sXY+nSymTen*sXX]\
416 + ddg_dtmp[SKEY + 3*SKEY]*ds[sXX]*ds[sXY] + ddg_dtmp[SKEY + 3*TARGKEY]*dtarg[sXX]*ds[sXY] + ddg_dtmp[SKEY + 3*J3KEY]*dJ3[sXX]*ds[sXY]\
417 + ddg_dtmp[TARGKEY + 3*SKEY]*ds[sXX]*dtarg[sXY] + ddg_dtmp[TARGKEY + 3*TARGKEY]*dtarg[sXX]*dtarg[sXY] + ddg_dtmp[TARGKEY + 3*J3KEY]*dJ3[sXX]*dtarg[sXY]\
418 + ddg_dtmp[J3KEY + 3*SKEY]*ds[sXX]*dJ3[sXY] + ddg_dtmp[J3KEY + 3*TARGKEY]*dtarg[sXX]*dJ3[sXY] + ddg_dtmp[J3KEY + 3*J3KEY]*dJ3[sXX]*dJ3[sXY];
419
420 dr[sXY+ nSymTen*sYY] = dg_dtmp[TARGKEY]*ddtarg[sXY+nSymTen*sYY] + dg_dtmp[J3KEY]*ddJ3[sXY+nSymTen*sYY]\
421 + ddg_dtmp[SKEY + 3*SKEY]*ds[sYY]*ds[sXY] + ddg_dtmp[SKEY + 3*TARGKEY]*dtarg[sYY]*ds[sXY] + ddg_dtmp[SKEY + 3*J3KEY]*dJ3[sYY]*ds[sXY]\
422 + ddg_dtmp[TARGKEY + 3*SKEY]*ds[sYY]*dtarg[sXY] + ddg_dtmp[TARGKEY + 3*TARGKEY]*dtarg[sYY]*dtarg[sXY] + ddg_dtmp[TARGKEY + 3*J3KEY]*dJ3[sYY]*dtarg[sXY]\
423 + ddg_dtmp[J3KEY + 3*SKEY]*ds[sYY]*dJ3[sXY] + ddg_dtmp[J3KEY + 3*TARGKEY]*dtarg[sYY]*dJ3[sXY] + ddg_dtmp[J3KEY + 3*J3KEY]*dJ3[sYY]*dJ3[sXY];
424
425 dr[sXY+ nSymTen*sZZ] = dg_dtmp[TARGKEY]*ddtarg[sXY+nSymTen*sZZ] + dg_dtmp[J3KEY]*ddJ3[sXY+nSymTen*sZZ]\
426 + ddg_dtmp[SKEY + 3*SKEY]*ds[sZZ]*ds[sXY] + ddg_dtmp[SKEY + 3*TARGKEY]*dtarg[sZZ]*ds[sXY] + ddg_dtmp[SKEY + 3*J3KEY]*dJ3[sZZ]*ds[sXY]\
427 + ddg_dtmp[TARGKEY + 3*SKEY]*ds[sZZ]*dtarg[sXY] + ddg_dtmp[TARGKEY + 3*TARGKEY]*dtarg[sZZ]*dtarg[sXY] + ddg_dtmp[TARGKEY + 3*J3KEY]*dJ3[sZZ]*dtarg[sXY]\
428 + ddg_dtmp[J3KEY + 3*SKEY]*ds[sZZ]*dJ3[sXY] + ddg_dtmp[J3KEY + 3*TARGKEY]*dtarg[sZZ]*dJ3[sXY] + ddg_dtmp[J3KEY + 3*J3KEY]*dJ3[sZZ]*dJ3[sXY];
429
430 dr[sXY+ nSymTen*sYZ] = dg_dtmp[TARGKEY]*ddtarg[sXY+nSymTen*sYZ] + dg_dtmp[J3KEY]*ddJ3[sXY+nSymTen*sYZ]\
431 + ddg_dtmp[SKEY + 3*SKEY]*ds[sYZ]*ds[sXY] + ddg_dtmp[SKEY + 3*TARGKEY]*dtarg[sYZ]*ds[sXY] + ddg_dtmp[SKEY + 3*J3KEY]*dJ3[sYZ]*ds[sXY]\
432 + ddg_dtmp[TARGKEY + 3*SKEY]*ds[sYZ]*dtarg[sXY] + ddg_dtmp[TARGKEY + 3*TARGKEY]*dtarg[sYZ]*dtarg[sXY] + ddg_dtmp[TARGKEY + 3*J3KEY]*dJ3[sYZ]*dtarg[sXY]\
433 + ddg_dtmp[J3KEY + 3*SKEY]*ds[sYZ]*dJ3[sXY] + ddg_dtmp[J3KEY + 3*TARGKEY]*dtarg[sYZ]*dJ3[sXY] + ddg_dtmp[J3KEY + 3*J3KEY]*dJ3[sYZ]*dJ3[sXY];
434
435 dr[sXY+ nSymTen*sZX] = dg_dtmp[TARGKEY]*ddtarg[sXY+nSymTen*sZX] + dg_dtmp[J3KEY]*ddJ3[sXY+nSymTen*sZX]\
436 + ddg_dtmp[SKEY + 3*SKEY]*ds[sZX]*ds[sXY] + ddg_dtmp[SKEY + 3*TARGKEY]*dtarg[sZX]*ds[sXY] + ddg_dtmp[SKEY + 3*J3KEY]*dJ3[sZX]*ds[sXY]\
437 + ddg_dtmp[TARGKEY + 3*SKEY]*ds[sZX]*dtarg[sXY] + ddg_dtmp[TARGKEY + 3*TARGKEY]*dtarg[sZX]*dtarg[sXY] + ddg_dtmp[TARGKEY + 3*J3KEY]*dJ3[sZX]*dtarg[sXY]\
438 + ddg_dtmp[J3KEY + 3*SKEY]*ds[sZX]*dJ3[sXY] + ddg_dtmp[J3KEY + 3*TARGKEY]*dtarg[sZX]*dJ3[sXY] + ddg_dtmp[J3KEY + 3*J3KEY]*dJ3[sZX]*dJ3[sXY];
439
440 dr[sXY+ nSymTen*sXY] = dg_dtmp[TARGKEY]*ddtarg[sXY+nSymTen*sXY] + dg_dtmp[J3KEY]*ddJ3[sXY+nSymTen*sXY]\
441 + ddg_dtmp[SKEY + 3*SKEY]*ds[sXY]*ds[sXY] + ddg_dtmp[SKEY + 3*TARGKEY]*dtarg[sXY]*ds[sXY] + ddg_dtmp[SKEY + 3*J3KEY]*dJ3[sXY]*ds[sXY]\
442 + ddg_dtmp[TARGKEY + 3*SKEY]*ds[sXY]*dtarg[sXY] + ddg_dtmp[TARGKEY + 3*TARGKEY]*dtarg[sXY]*dtarg[sXY] + ddg_dtmp[TARGKEY + 3*J3KEY]*dJ3[sXY]*dtarg[sXY]\
443 + ddg_dtmp[J3KEY + 3*SKEY]*ds[sXY]*dJ3[sXY] + ddg_dtmp[J3KEY + 3*TARGKEY]*dtarg[sXY]*dJ3[sXY] + ddg_dtmp[J3KEY + 3*J3KEY]*dJ3[sXY]*dJ3[sXY];
444
445}
r
Double r
Definition Headers.h:83
f
Double f
Definition Headers.h:64
s
Double s
Definition Headers.h:84
phi
Double phi
Definition Headers.h:76
psi
Double psi
Definition Headers.h:78
df
double df(double C, double b, double a, int q, int r)
Definition analyticalSolutions.c:2209
c
#define c(i)
Definition jf.h:21
tresca
void tresca(const double &phi, const double &psi, const double &c, const double *stress, double &f, double *df, double &g, double *r, double *dr)
Definition tresca.h:2
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